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  <section id="module-sympy.holonomic">
<span id="holonomic"></span><span id="holonomic-docs"></span><h1>Holonomic<a class="headerlink" href="#module-sympy.holonomic" title="Permalink to this headline">¶</a></h1>
<p>The <a class="reference internal" href="#module-sympy.holonomic" title="sympy.holonomic"><code class="xref py py-mod docutils literal notranslate"><span class="pre">holonomic</span></code></a> module is intended to deal with holonomic functions along
with various operations on them like addition, multiplication, composition,
integration and differentiation. The module also implements various kinds of
conversions such as converting holonomic functions to a different form and the
other way around.</p>
<section id="contents">
<h2>Contents<a class="headerlink" href="#contents" title="Permalink to this headline">¶</a></h2>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="about.html">About Holonomic Functions</a><ul>
<li class="toctree-l2"><a class="reference internal" href="about.html#definition">Definition</a></li>
<li class="toctree-l2"><a class="reference internal" href="about.html#references">References</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="represent.html">Representation of holonomic functions in SymPy</a><ul>
<li class="toctree-l2"><a class="reference internal" href="represent.html#holonomicfunction">HolonomicFunction</a></li>
<li class="toctree-l2"><a class="reference internal" href="represent.html#differentialoperator">DifferentialOperator</a></li>
<li class="toctree-l2"><a class="reference internal" href="represent.html#differentialoperators">DifferentialOperators</a></li>
<li class="toctree-l2"><a class="reference internal" href="represent.html#differentialoperatoralgebra">DifferentialOperatorAlgebra</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="operations.html">Operations on holonomic functions</a><ul>
<li class="toctree-l2"><a class="reference internal" href="operations.html#addition-and-multiplication">Addition and Multiplication</a></li>
<li class="toctree-l2"><a class="reference internal" href="operations.html#integration-and-differentiation">Integration and Differentiation</a></li>
<li class="toctree-l2"><a class="reference internal" href="operations.html#composition-with-polynomials">Composition with polynomials</a></li>
<li class="toctree-l2"><a class="reference internal" href="operations.html#convert-to-holonomic-sequence">Convert to holonomic sequence</a></li>
<li class="toctree-l2"><a class="reference internal" href="operations.html#series-expansion">Series expansion</a></li>
<li class="toctree-l2"><a class="reference internal" href="operations.html#numerical-evaluation">Numerical evaluation</a></li>
<li class="toctree-l2"><a class="reference internal" href="operations.html#convert-to-a-linear-combination-of-hypergeometric-functions">Convert to a linear combination of hypergeometric functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="operations.html#convert-to-a-linear-combination-of-meijer-g-functions">Convert to a linear combination of Meijer G-functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="operations.html#convert-to-expressions">Convert to expressions</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="convert.html">Converting other representations to holonomic</a><ul>
<li class="toctree-l2"><a class="reference internal" href="convert.html#converting-hypergeometric-functions">Converting hypergeometric functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="convert.html#converting-meijer-g-functions">Converting Meijer G-functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="convert.html#converting-symbolic-expressions">Converting symbolic expressions</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="uses.html">Uses and Current limitations</a><ul>
<li class="toctree-l2"><a class="reference internal" href="uses.html#integration">Integration</a></li>
<li class="toctree-l2"><a class="reference internal" href="uses.html#limitations">Limitations</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="internal.html">Internal API</a></li>
</ul>
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</section>
</section>


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